{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 46,
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数据生成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "T = 1000 # 总共产生1000个点\n",
    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
    "x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))\n",
    "d2l.plot(time, [x], 'time', 'x', xlim=[1, 1000], figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau = 4# 定义了时间窗口的大小，意味着使用过去4个时间点的数据来预测下一个时间点的值\n",
    "features = torch.zeros((T - tau, tau))\n",
    "for i in range(tau):\n",
    "    features[:, i] = x[i: T - tau + i]\n",
    "\"\"\"\n",
    "特征数据样子大致如下：\n",
    "[0  ,1  ,2  ,3]\n",
    ". . . .......\n",
    ". . . .......\n",
    "[996,997,998,999]\n",
    "\"\"\"    \n",
    "labels = x[tau:].reshape((-1, 1))#从第五个元素往后开始排，意思是前四个预测这个标签\n",
    "batch_size, n_train = 16, 600\n",
    "# 只有前n_train个样本用于训练\n",
    "train_iter = d2l.load_array((features[:n_train], labels[:n_train]),\n",
    "batch_size, is_train=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型构建"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**就用简单的多层感知机**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "#初始化\n",
    "def init_parameters(m):\n",
    "    if type(m)==nn.Linear:\n",
    "        nn.init.xavier_uniform_(m.weight)\n",
    "#定义模型\n",
    "def mlp():\n",
    "    net=nn.Sequential(\n",
    "        nn.Linear(4,10),\n",
    "        nn.ReLU(),     \n",
    "        nn.Linear(10,1)\n",
    "    )\n",
    "    net.apply(init_parameters)\n",
    "    return net\n",
    "#损失函数\n",
    "loss=nn.MSELoss(reduction=\"none\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1轮训练，损失： 0.0675941118101279\n",
      "2轮训练，损失： 0.05485421404242516\n",
      "3轮训练，损失： 0.05322145688037078\n",
      "4轮训练，损失： 0.05243650294840336\n",
      "5轮训练，损失： 0.05180377329389254\n",
      "6轮训练，损失： 0.050883536636829374\n",
      "7轮训练，损失： 0.050551199366648994\n",
      "8轮训练，损失： 0.050047005712985995\n",
      "9轮训练，损失： 0.05103823781013489\n",
      "10轮训练，损失： 0.04948678486049175\n"
     ]
    }
   ],
   "source": [
    "def train(net,train_iter,loss,epochs,lr):\n",
    "    trainer=torch.optim.Adam(net.parameters(),lr)\n",
    "    for epoch in range(epochs):\n",
    "        for X,y in train_iter:\n",
    "            trainer.zero_grad()\n",
    "            l=loss(net(X),y)\n",
    "            l.sum().backward()\n",
    "            trainer.step()\n",
    "        print(f'{epoch+1}轮训练，损失：',d2l.evaluate_loss(net,train_iter,loss))\n",
    "net=mlp()\n",
    "train(net,train_iter,loss,10,0.01)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 预测"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "预测的趋势大差不差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "onestep_preds = net(features)#直接喂入所有训练集\n",
    "d2l.plot([time, time[tau:]],\n",
    "[x.detach().numpy(), onestep_preds.detach().numpy()], 'time',\n",
    "'x', legend=['data', '1-step preds'], xlim=[1, 1000],\n",
    "figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([996, 1])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "onestep_preds.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 出现的挑战"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当前预测效果不错：单步预测（即预测下一个时间点的值）效果很好，尽管数据量很大。\n",
    "\n",
    "面临的问题：当观察到的数据序列只到达604时，他们需要进行多步预测（即预测未来多个时间点的值），而不是只预测下一个时间点。\n",
    "\n",
    "多步预测的要求：为了进行多步预测，必须使用之前的预测结果，而不是直接使用原始数据。这意味着需要依赖于模型的输出，而不是直接从已有的数据中获取信息。\n",
    "\n",
    "总的来说，问题在于如何在数据序列到达一定点时，利用已有的预测结果来进行更长时间的预测，而不是仅仅依赖于过去的数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "multistep_preds = torch.zeros(T)\n",
    "multistep_preds[: n_train + tau] = x[: n_train + tau]#前604个数先录进去\n",
    "for i in range(n_train + tau, T):#预测605到1000的数\n",
    "    multistep_preds[i] = net(\n",
    "        multistep_preds[i - tau:i].reshape((1, -1))\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "开始点(训练好的模型从605开始走)走步走的少，预测的就不准了"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
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   "source": [
    "d2l.plot([time, time[tau:], time[n_train + tau:]],\n",
    "[x.detach().numpy(), onestep_preds.detach().numpy(),\n",
    "multistep_preds[n_train + tau:].detach().numpy()], 'time',\n",
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   "cell_type": "markdown",
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   "source": [
    "**基于k = 1, 4, 16, 64，通过对整个序列预测的计算，让我们更仔细地看一下k步预测的困难。**"
   ]
  },
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   "metadata": {},
   "source": [
    "64步"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
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      "text/plain": [
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   "source": [
    "max_steps = 64\n",
    "features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))\n",
    "# 列i（i<tau）是来自x的观测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau):#前四列填充\n",
    "    features[:, i] = x[i: i + T - tau - max_steps + 1]\n",
    "# 列i（i>=tau）是来自（i-tau+1）步的预测，其时间步从（i）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau, tau + max_steps):\n",
    "    features[:, i] = net(features[:, i - tau:i]).reshape(-1)\n",
    "\n",
    "steps = (1, 4, 16, 64)#4-67列填充\n",
    "d2l.plot([time[tau + i - 1: T - max_steps + i] for i in steps],\n",
    "[features[:, (tau + i - 1)].detach().numpy() for i in steps], 'time', 'x',\n",
    "legend=[f'{i}-step preds' for i in steps], xlim=[5, 1000],\n",
    "figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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